Simplify complex physics and math concepts with this easy guide to Lagrange multipliers! In this video, we explain how to calculate constraint forces in polar coordinates using step-by-step examples ...

The Georgia High School Association placed schools into classifications for the 2026-27 and 2027-28 academic years this week. Schools may appeal their placement or petition to play higher or low in ...

SHARPy is a nonlinear aeroelastic analysis package originally developed at the Department of Aeronautics, Imperial College London. It can be used for the structural, aerodynamic and aeroelastic ...

Complex systems can often be conceptualized at both a microlevel (for example, molecules of a gas) and a macrolevel (for example, pressure and temperature of the gas). Bottom–Up, agent-based ...

Abstract: A common formulation of constrained reinforcement learning involves multiple rewards that must individually accumulate to given thresholds. In this class of problems, we show a simple ...

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30–40 years ...

All through human civilization, optimization has played a major role, from aerodynamics to airline scheduling, delivery routing, and telecommunications decoding. Optimization is receiving increasing ...

Robert P. Crease is fascinated by a biography of quantum physicist Hugh Everett III, the difficult man behind one of the most logical and bizarre ideas in the history of human thought. The 'many ...